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I am playing some pieces in various keys; for example this one (from William Leavitt - Melodic Rhythms For Guitar):

exercise

I want to play it in a certain position (not using open strings), such that each finger is assigned to a fret. It turns out that this example can be played at position 3:

---------------------------------------...
-4-3---4-----3-------------------------...
-----5---------3---------5-----------3-...
---------------------5-----6-----3-----...
-----------------------6-----------5---...
---------------------------------------...

However, if I try playing it at position 4, I'll soon discover that I need an uncomfortable stretch:

-----------------
-4-----4---------
---7-5-------7---
---------------8- < problem!
-----------------
-----------------

Are there rules of thumb that let me quickly determine a possible playing position from the key?

Like (for example)

Key E♭? Play at position 3

Key Am? Play at position 5

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Each melody will differ, as the range will be different. So, no rule of thumb, except check the highest and lowest notes, and check through each note as it comes.And bear in mind that any accidentals may throw you out by a fret up or down.

Using a four fret encompass works for, for instance, a full two octave (plus 3 or 4 extra notes). Take A major,(4-7) starting at 5th fret bottom string. Assuming you're not going to find F on 4th string, it all works. Take A natural minor, though,(5-8) and to do the same involves moving down to B on the third string, so you're out of span. Make it A harmonic and the same occurs on top string for G#. So, almost all melodies will present a move out of the 4 fret span, if this is what you seek.

What most players end up doing is sharing a melody with two adjacent shapes, sliding between them as ans when. Obviously you'll find some melodies that fit your mould, but I don't think there's a formula that applies to give the answer. Play in several, and find those with least movement - or play up the dusty end of the neck, where a 5 fret stretch is less problematic.

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Are there rules of thumb that let me quickly determine a possible playing position from the key?

Really depends on the song/exercise you're trying to play. I don't there is a rule of thumb for things like this. You might find two songs that are in the same key, but for some reason or another, they aren't easy to play in the same position.

What I do and what I believe really helps is to try to figure it out by yourself. Try it on a couple of different positions and see what position fits for every song. This might not work on the next song that is in the same, but it will help you to learn your instrument and you'll be able to play in most of the positions, because you'll have had practice in them.

Also, this way you'll be able to play part of the exercise in many different positions. This will help you improvise (if you are interested in it).

Of course there are some stuff you should take into consideration. Like for instance, if your exercise/song is in Eb, and you are using standard tuning on your guitar, you (most likely) wouldn't start from the low E string, because it is a semitone higher than the desired tonic. You can start from F, the second of the scale, if you are going for something like that, but most likely, you are going to start from a higher position.

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